Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints-Reference-Cited by-同舟云学术

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

Published:2018-01-11 Issue:3 Volume:13 Page:219-255
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Arroyo-Rabasa Adolfo¹^ORCID,De Philippis Guido²,Rindler Filip³^ORCID

Affiliation:

1. Mathematisches Institut , Universität Leipzig , Augustusplatz 10, 04109 Leipzig , Germany

2. Scuola Internazionale Superiore di Studi Avanzati , Via Bonomea 265, 34136 Trieste , Italy

3. Mathematics Institute , University of Warwick , Coventry CV4 7AL , United Kingdom

Abstract

Abstract We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary order). These results generalize several known lower semicontinuity and relaxation theorems for BV, BD, and for more general first-order linear PDE side constrains. Our proofs are based on recent progress in the understanding of singularities of measure solutions to linear PDEs and of the generalized convexity notions corresponding to these PDE constraints.

Funder

Engineering and Physical Sciences Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2017-0003/pdf

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